Bunuel wrote:
Official Solution:
Statement (1) by itself is insufficient. We do not know the scale of the triangle. If 0.001 is small compared to the sides of the triangle then \(AC\) almost equals \(AB + BC\) and thus angle \(ABC\) is obtuse. But if the sides are all small, 0.001 might not indicate that \(AC\) is about equal to \(AB + BC\).
Statement (2) by itself is sufficient. It means that \(\angle ABC = \angle BCA\). A triangle cannot have two angles that are both greater than 90 degrees.
Answer: B
Hi
Bunuel,
I am not clear about the reasoning for Statement 1. We know it as a rule that any side in a triangle cannot be more than the some of the other two sides. I am unable visualize how will angle ABC change based on a change in scale of the triangle as you mentioned.
If 0.001 is small compared to the sides of the triangle then \(AC\) almost equals \(AB + BC\) and thus angle \(ABC\) is obtuse. But if the sides are all small, 0.001 might not indicate that \(AC\) is about equal to \(AB + BC\).Here can we be absolutely sure that if 0.001 is small compared to the sides of the triangle then angle ABC will be obtuse?
I understand that the angles depend on the length of the sides opposite the angle but how do we know for sure that for a large side length AC, angle ABC will be obtuse. Same question for the opposite case assuming very small lengths.
Regards,
Udit